SPH4U UNIT 3 TEST GRAVITATIONAL AND ELECTRIC FIELDS Part A Knowledge and Understanding [20 marks) Multiple Choice Use a CAPITAL letter that best completes the statement or answers the question 1. The gravitational force between two spherical masses is Fi. Which of the following would decrease the gravitational force between the objects to 0.25F1? a) decreasing the mass of one object to half its original value. b) imereasing the distance by a factor of 2. c) decreasing the distance to 0.5 the original value. d) mereasing the mass of both objects by a factor of 2. 2. For a given mass, m, and a given distance. d, separating you and the object. which of the following would exert a stronger gravitational force on vou? a) an object of mass Tm a distance 15d away. b) an object of mass 9m a distance 5d away. c) an object of mass 8m a distance 3d away. d) an object of mass 12m a distance 4d away. 3. A small object has an excess of 4.7 x 10! electrons. The magnitude of the electric potential at a distance of 0.200 m from the object would be: (e= 1.6 x 102*C) a) 2.7x 105V b) 3.4 x 10V ) 2.1x 10 d) 2.6 x 10*V e) 1.2x 1077V 4. A satellite is in a circular orbit around the Earth at an altitude of 650 km. What orbital speed must th satellite maintain to stay in orbit at this altitude? a) 5.7 X 10' m/'s c) 2.5 X 10# m/s b) 7.5 X 10' m/s d) 7.9 X 10# m/'s + 20 cm 20 cm 5. Four charged spheres, A, D. P, and T are arranged as shown above. Sphere A has a charge of +q. sphere D has a charge of -q. sphere P has a charge of +0.5q, and sphere T has a charge of -2q. Which two spheres exert the largest force on each other (magnitude only)? a. A and D d. P and D b. D and T e. Pand T c. A and P6. An electron e and a proton p are simultaneously released e from rest in a uniform electric field &, as shown. Assume P that the particles are sufficiently far apart so that the only ' - e force acting on each particle after it 1s released 1s that due R Z to the electric field. At a later time when the particles are e still in the field. the electron and the proton will have the -',_._.L,___ same B - o direction of motion speed displacement magnitude of acceleration magnitude of force acting on them 2 ) +20 -0 7. Two identical conducting spheres are charged to +20Q and Q. respectively. and are separated by a distance d (much greater than the radii of the spheres) as shown above. The magnitude of the force of attraction on the left sphere is F1. After the two spheres are made to touch and then are separated by distance d. the magnitude of the force on the left sphere is Fo. Which of the following relationships is correct? 00 oTw a. 2Fi=F b. Fi=F2 c. F1=2F d. Fi=4F e. F1=8F 8. The electric field at a distance of 1.0 m from a charged sphere 1s 100 N/C. At what distance from the sphere will the electric field be 50 N/C? a) 1.1 m. c) 2.0 m. b) 14m d) 4.0 m. 9. Two metal spheres that are initially uncharged are mounted on insulating stands, as shown. A negatively charged rubber rod is brought close to. but does not make contact with, sphere 1. Sphere 2 1s then brought close to 1 on the side opposite to the rubber rod. Sphere 2 is allowed to touch 1 and then 1s removed some distance away. The rubber rod is then moved far away from 1 and 2 What are the final charges on the spheres? Sphere 1 Sphere 2 a) Negative Negative b) Negative Positive ) Positive Negative d) Positive Positive 10. The electric potential due to a point charge at a point depends on a) the direction of the electric field. ) the velocity of the point charge. b) the distance from the point charge d) the mass of the point charge. Short Answer [10 marks] 11. Draw appropriate electric field lines for the charges below, showing the NET electric field for this region of space. (5 marks) 12. When considering the forces acting between two charged objects, explain why we would typically only consider the Coulomb's force and not the force of gravity. [3 marks] 13. A student rubs a balloon against her hair. She then places the side of the balloon against a wall and the balloon sticks to the wall. Explain why the balloon sticks to the wall. [2 marks] Part B Communication [10 marks] Communication throughout the test will be evaluated on 1) significant digits (avoid rounding off errors) 2) proper use of units 3) well-labelled diagrams 4) organized, neat and legible 5) Show all work with concluding statements. Level 4 Level 3 Level 2 Level 1 Communicates for different Communicates for different Communicates for different Communicates for different audiences and purposes with a high | audiences and purposes with audiences and purposes with some audiences and purposes with degree of effectiveness considerable effectiveness. effectiveness limited effectiveness Uses conventions, vocabulary, and Uses conventions, vocabulary, and Uses conventions, vocabulary, and Uses conventions, vocabulary, and terminelogy of the discipline with a | terminology of the discipline with terminology of the discipline with terminology of the discipline with high degree of effectiveness considerable effectiveness some effectiveness limited effectiveness Part C Thinking (Full Selution is required) [10 marks] 14. Robert Millikan received a Nobel Prize for determining the charge on the electron. To do this, he setup a potential difference between two horizontal parallel metal plates. He then sprayed drops of oil between the plates and adjusted the potential difference until drops of a certain size remained suspended at rest between the plates. as shown above. Suppose that when the potential difference between the plates is adjusted until the electric field is 1.00 x 10* N/C downward, a certain drop with a mass of 3.27 = 107 kg remains suspended. a. What 1s the charge on this drop? (4 marks) b. If the distance between the plates is 0.010 m, what is the battery's potential? (3 marks) . The oil in the drop slowly evaporates while the drop is being observed. but the charge on the drop remains the same. Indicate whether the drop remains at rest, moves upward, or moves downward. Explain briefly. using equations to support your answer. (3 marks) s are Reguired) [20 marks] 14. An electron 1s released from rest at the negative plate in a parallel plate apparatus kept under vacuum and maintained a potential difference of 5.0 X 10! V. With what speed does the electron collide with the positive plate? (m=9.11x10"kg, q=-1.6x10"C) [2 marks] 15. A 1500-kg satellite 15 moved from an orbit of 2 Earth radii to an orbit of 2.5 Earth radii. How much energy is required to accomplish this? (Me=5.98 x 10 kg, Re = 6.38 x 10 m) (4 marks) 16. Two masses of 5.0 g each are suspended from thin strings and a charge is placed on each. The result is shown in the diagram below. If the angle between each string and the vertical is 157 and the length of the string 15 35 em, determine the charge . (4 marks) 17. Electrons are accelerated through a potential difference, Vo = 120 V, before exiting and being subjected to a new set of parallel plates. The electrons enter this region 5.0 em from the bottom plate, and hit this bottom plate a distance of 5.0 em in. If the total plate separation of this second set of plates 1s 8.0 em, determine the voltage of the second source AND draw this source in, clearly showing the positive vs negative terminals of the battery. (m=9.11 10 kg, q = 1.6x10"C) (10 marks)